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Understanding quantitative variables is pivotal in educational research, as they are integral to quantitative analysis. Quantitative variables are data that can be quantified or measured and are expressed numerically. These variables can appear in various forms such as test scores, response times, or any numerical data that are collected through research.

In the context of our research example, the quantitative variable is the student's score on a reading test. This type of data is invaluable because it allows researchers to perform statistical analyses, which can include measures of central tendency (like the mean or median) and dispersion (such as standard deviation). Quantitative variables can represent different levels of measurement, including nominal, ordinal, interval, and ratio scales.

For instance, a reading test score is likely an interval or ratio variable, as it not only ranks students (as would be the case with ordinal data), but also quantifies the exact difference in reading ability (which nominal data do not). Such precise data allows the researcher to make comparisons and draw significant conclusions about the effectiveness of the new teaching method.

Experimental units are essential foundations of any empirical study. They are the smallest division of analysis which receives the intervention or treatment in an experiment. In essence, an experimental unit is what or who the experiment is conducted on. This can range from individual participants, such as students or patients, to larger entities, such as classrooms or hospitals, depending on the scale of the study.

In our selected research scenario, the individual student serves as the experimental unit. The new reading teaching method is applied to each student, and their test scores before and after the intervention are observed and recorded. The use of individual students as the experimental unit allows the researcher to control the variables more tightly and to make more precise statements about the cause and effect relationship between the teaching method and the reading test scores.

Defining the population of interest is a fundamental step in conducting research. It refers to the entire group of individuals or subjects to which the researcher aims to generalize the findings. This population encompasses all members who share a set of characteristics that the experiment or study is addressing.

In the exercise mentioned, the population of interest is all deaf students who could potentially benefit from the new method of teaching reading. While the study may only include a sample of the entire population due to practical constraints, the intention is to draw inferences that are applicable to the wider population. Therefore, selecting a representative sample becomes crucial. The effectiveness of the new teaching method, as observed through the sample's collected data, is used to make an educated guess about its potential success or failure within the whole population of deaf students.